Problem: Umaima is 4 years older than Emily. Eight years ago, Umaima was 5 times older than Emily. How old is Umaima now?
Solution: We can use the given information to write down two equations that describe the ages of Umaima and Emily. Let Umaima's current age be $u$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $u = e + 4$ Eight years ago, Umaima was $u - 8$ years old, and Emily was $e - 8$ years old. The information in the second sentence can be expressed in the following equation: $u - 8 = 5(e - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = u - 4$ . Substituting this into our second equation, we get the equation: $u - 8 = 5($ $(u - 4)$ $ -$ $ 8)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $u - 8 = 5u - 60$ Solving for $u$ , we get: $4 u = 52$ $u = 13$.